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Minor surface meshes
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Umberto Zerbinati committed Jul 8, 2024
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5 changes: 2 additions & 3 deletions docs/src/utils/firedrake/surfaces.py.rst
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Expand Up @@ -24,7 +24,7 @@ Once we have generated a surface mesh using Netgen, we can simply pass it to Fir
from firedrake import *
mesh = Mesh(Mesh(ngmesh).curve_field(3))

We begin defining the initial condition for the problem, in particular, we will consider a Gaussian function centered at a point on the torus. ::
We begin defining the initial condition for the problem, in particular, we will consider a Gaussian bump centered at a point on the torus. ::

x, y, z = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 3)
Expand All @@ -34,13 +34,12 @@ We begin defining the initial condition for the problem, in particular, we will
out = VTKFile("output/heat.pvd")
out.write(u, time=0.0)

We now use [Irksome](https://www.firedrakeproject.org/Irksome), to describe the time-dependent problem we aim to solve, i.e.
We now use `Irksome<https://www.firedrakeproject.org/Irksome>_`, to describe the time-dependent problem we aim to solve, i.e.

.. math::
\begin{align*}
\frac{\partial u}{\partial t} - \nabla \cdot \nabla u &= 0 \quad \text{in} \quad \Omega \times (0, T], \\
u &= 0 \quad \text{on} \quad \partial \Omega \times (0, T], \\
u &= u_0 \quad \text{at} \quad t = 0.
\end{align*}
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